Personally I wouldn't know, never having used Photoshop, however I would have thought a possibility would be to use Phil Harvey's EXIFTOOL to cope the exif data from one file in the pre-stack and paste/write it into the final stacked photo.

Off out to prune some bushes now, so don't have time to look up the syntax myself, but it's a very powerful program.

Also look up Exiftool GUI in your favourite search engine, for a more accessible interface.